Coordinate system

Coordinate system
Sudarto
Laboratorium Pedologi dan Sistem Informasi Sumberdaya Lahan
Jurusan Tanah, Fakultas Pertanian Universitas Brawijaya

Earth’s surface is three-dimensional
• Feature location expressed in latitude and
longitude

Maps are two-dimensional
• Map feature location identified with x- and y-
coordinates

How do we register the three-dimensional
Earth to the two-dimensional map?
• Location reference
system for spatial
features on earth’s
surface
• Angular measurement
from an origin to a
given point
• Latitude (parallels)
• Longitude (meridians)
Parallels of Latitude Meridians of
Longitude Graticular Network
b: Latitude
a: longitude
A mathematical model of the earth must be
selected. Ellipsoid / Spheroid
The mathematical model must be related
to real-world features. Datum
Real-world features must be projected with
minimum distortion from a round earth to a
flat map; and given a grid system of
coordinates. Map Projection
A mathematical model of the earth must be
selected
Simplistic - A round ball having a radius big
enough to approximate the size of the earth.
Reality - Spinning planets swell at the equator
with correlative flattening at the poles. e.g.
 Shape
of Earth not perfectly circular
 Ellipsoid
 Major axis (a)
 Minor axis (b)
 Flattening (f)
(a-b)/a
 If a=b, the ellipsoid is a spheroid
A mathematical approximation to the shape of the Earth
Semi minor axis
Semi mayor axis
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The Geoid is an equipotential surface of the Earth gravity
field that most closely approximates the mean sea level.
The ellipsoid is an approximation to the Geoid.
Using different approximations will result in different
accuracies.
Coordinate systems are applied to the simpler
model of a ellipsoid / spheroid.
The problem is that actual measurements of
location conform to the geoid surface and have to
be mathematically recalculated to positions on
the ellipsoid / spheroid.
A mathematical model must be related to
real-world features

A smooth mathematical surface that fits
closely to the mean sea level surface
throughout the area of interest. The surface
to which the ground control measurements
are referred.

•Provides a frame of reference for measuring
locations on the surface of the earth.
A Datum:
is a model of the earth and describes the
relationship (origin & orientation) between
the coordinate system and the Earth.
A Datum is defined by:
The size & shape of the model (Ellipsoid) The
position & orientation of the model (Ellipsoid)
in relation to the physical surface of the Earth.

To determine latitude and longitude, surveyors level
their measurements down to a surface called a geoid.
The geoid is the shape that the earth would have if all its
topography were removed.

Or more accurately, the shape the earth would have if
every point on the earth's surface had the value of
mean sea level.

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The earth's spheroid deviates slightly for different regions of
the earth.
Using a wrong datum can result in considerable position
errors.
The definition of a datum can be based on local or global
considerations
Different nations and agencies may use different Datums
• GRS80 (North America)
• Clark 1866 (North America
• WGS84 (GPS World-wide)
• International 1924 (Europe)
• Bessel 1841 (Europe)
The datum on which GPS coordinates
are based and probably the most
common datum for GIS data sets with
global extent.
Geodetic Latitude & Longitude on an ellipsoid
(Lat φ, Long λ, Ellipsoid height h)

Horizontal datums are the reference values
for a system of location measurements.

Vertical datums are the reference values for
a system of elevation measurements.
Chosen Ellipsoid
Geodetic Coordinate System
(Lat and Long)
The Height is defined as the distance from a chosen
reference system along the perpendicular to a
surface: Geoid & ellipsoid
 Ellipsoid (Ellipsoid height h):
• a mathematical reference
• Provides ellipsoidal heights
 The Geoid (Orthometric height H):
• a physical reference
• Provides Orthometric Heights (elevation)
 GPS provides ellipsoidal heights
H: orthometric height (elevation)
h: ellipsoidal height
N: geoid height
H=h-N
The job of a vertical datum is to define where
zero elevation is, this is usually done by
determining mean sea level.
Chosen Geoid
Chosen Ellipsoid
Geoide Height (N)
Ellipsoid height (h)
Orthometric Height (H: Elevation)
Not uniform:
– Distances and measures
are not accurate
Distance of 60° long at 40° latitude
1° longitude:
– Equator= 111 km
– 60° lat. = 55.8 km
– 90° lat. = 0km
Distance of 60° long at equator
Projecting a Sphere Onto a Plane
Curved Earth
Geographic coordinates: f, l
(Latitude & Longitude)
Flat Map
Cartesian coordinates: x,y
(Easting & Northing)
Real-world features must be projected with minimum
distortion from a round earth to a flat map; and given a
grid system of coordinates.
Y
X
(Xo,Yo)
(ooλo)
A map projection transforms latitude and longitude
locations to x,y coordinates.
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Map projection is the process of transforming a 3D
world into 2D map.
Map projection is based on Ellipsoid
We often use Spheroid model to illustrate the concept
Azimuthal projection
Conical projection
Cylindrical projection
tangent
secant
Different Projections Preserve Different
Properties of the Earth
•
•
•
•

Directions
Distances
Shapes
Areas
If some properties are maintained,
errors in others may be exaggerated
Mercator Projection
Transvrese Mercator Projection

Divide the world into sixty vertical strips, each
spanning 6 degrees of longitude.

Apply a custom Transverse Mercator
projection to each strip and use false eastings
and northings to make all projected
coordinates positive.
Universal Transverse Mercator (UTM)
Setia tempat di muka bumi terletak pada zone tertentu
Sampai ketemu minggu depan
 Selesaikan
tugas minggu yang lalu
 Lengkapi atribut database dengan:
 Koordinat (UTM) Y dan Y nya (bisa dilihat pada image
Google Earth yang sudah terkoreksi)
 Atribut lain yang terkait